King County Council members, moved by stories of mentally ill people held in jail or taken to emergency rooms because they weren’t getting the treatment they needed, voted Thursday to fund improved services by raising the sales tax by one-tenth of 1 percent.

If the council gives final approval as expected on Tuesday, the sales tax would rise from 8.9 cents to 9 cents on a $1 purchase in most parts of the county. The entire council took part in the operating-budget committee’s 6-3 vote.

The move would provide $54 million a year for services to people with mental illness or substance-abuse problems.

But even as supporters hailed the bill as a landmark in mental-health care, Councilmember Kathy Lambert, an early supporter of the tax, voted against the ordinance because it requires contracting agencies to sign “partnership agreements” with labor unions for employee-organizing drives.

Under that provision, sought by County Executive Ron Sims and the Service Employees International Union, the county’s six largest mental-health providers won’t receive any new tax dollars until they implement agreements with “a bona fide labor organization.”

Lambert, R-Redmond, choked up as she said the labor provision was “morally wrong” and legally dubious. When the roll was called, she voted, “Unfortunately, no.”

Larry Phillips, D-Seattle, defended the partnership agreements, saying mental-health counselors are overworked and underpaid. “It is simply not an effective and efficient use of funds to give a professional $15 an hour to manage a caseload of 60 individuals.”

Bob Ferguson, D-Seattle, and prime sponsor of the tax, said the labor language was toned down from Sims’ original draft, which would have held up collection of the tax until partnership agreements were signed.

“I told him it was a nonstarter, it wouldn’t work,” Ferguson said.

Jane Hague, of Bellevue, the only Republican to vote for the tax, called it “one of the finest pieces of legislation that this legislative body has ever dealt with. … We have an opportunity today to comprehensively deal with compassion for the frail and the vulnerable in our community, as well as their families.”

The King County Mental Health Provider Association asked the council to remove the labor-organizing provision, saying it violates federal law.

David Stone, CEO of Sound Mental Health (formerly Seattle Mental Health), said his agency’s board will decide whether to sign a partnership agreement, refuse the new tax funds, or challenge the law in court.

Stone said his agency supports workers’ right to organize but worries that signing a partnership agreement “connotes a message to employees that you’re not neutral on the question of whether they should or should not join a union.”

SEIU Local 1199NW organizer Jonathan Rosenblum defended the language. “It’s saying employees should have a free and fair choice,” he said. “Tell me who’s against having a free and fair choice.”